The grammar construction (structure, it is denoted in many grammars) IT'S (BEEN) + DAYS / WEEKS / MONTHS / etc. + SINCE is used to emphasise the length of time that has passed since a past event. The strict grammatical logic behind this construction determines the use of the Past Indefinite Tense in the SINCE clause of the construction.
Strictly speaking, the construction it has been a long time since has nothing to do with the grammar of the previous construction. Because, they are different in many essential elements of their semantics and grammar.
Any complex syntactical structure needs to be parsing with its main clause. Both discussions are lack completely of such essential step.
The main clause it has been a long time consists of it- impersonal structure in the Present Perfect Tense + the linking verb be + Noun Phrase with the Head Word, the noun, a time. In its turn, NP consists of long (adjective) and a time (noun, singular).
The category of the noun a time gives the exact meaning for the noun which is a period of time, either long or short, during which you do something or something happens.
The category of the noun a time is not the category of the noun time having the sense of something measured in days, weeks, months etc. as it is in the first mentioned construction here. That is why the category of the noun a time used in the construction makes it possible to use much more grammar tenses and constructions than the Past Indefinite Tense only.
Taking into account the sense of the noun a time, we can conclude that the subordinate clause with the conjunction since is not typical for such grammar construction because of semantical problems. It is better to use subordinate clause that can attribute the main clause to some complete meaning with some information about what somebody did during this undefined a long time or what happened during a long time. This is a possible view for a grammarian who is making conclusions on logic. But, it is other situation for a user of conversational speech with some known or presupposed contexts. So we have here the contradiction between the so called grammatical logic and the so called natural language.
To put it simply, the examples have no contexts that may explain for a student how to build subordinate clauses. Any of the options could be taken as right or wrong. And be backed up by numerous examples from the natural spoken language. Without specifying implied contexts.
There are the grammar constructions of the type as it is/was a long time since NP in BrE, and it has been a long time since NP in AmE. NPs function in the adverbial prepositional phrase in both constructions. There is such syntactic structure as cleft sentences with preparatory it that is used for emphasising some parts of sentences, which having the syntactic form of it is/was ...that.
Analysis of these syntactic constructions, while taking into account earlier conclusions, allows reasonably to believe that in the case of OP's examples we should deal with them as if they were the varieties of cleft sentences in order to observe the requirements of the grammatical logic.